Question

If 2x+ 3y = 17 and 4x-y =13, then xy =
​

Answer 1

$\large\underline{\sf{Solution-}}$

☆ Given pair of linear equations are

$\rm :\longmapsto\:2x + 3y = 17 - - - (1)$

and

$\rm :\longmapsto\:4x - y = 13 - - - (2)$

☆ We use elimination method to get the value of x and y.

☆ Multiply equation (1) by 2, we get

$\rm :\longmapsto\:4x + 6y = 34 - - - (3)$

☆ On Subtracting equation (2) from equation (3), we get

$\rm :\longmapsto\:7y = 21$

$\bf\implies \:y = 3 - - - (4)$

☆ On substituting value of y = 3 in equation (2), we get

$\rm :\longmapsto\:4x - 3 = 13$

$\rm :\longmapsto\:4x = 13 + 3$

$\rm :\longmapsto\:4x = 16$

$\bf\implies \:x = 4 - - - (5)$

Hence,

$\bf :\longmapsto\:xy = 4 \times3 = 12$

Additional Information :-

The Elimination Method

Step 1:

• Multiply each equation by a suitable number so that the two equations have the same leading coefficient. .

Step 2:

• Subtract the second equation from the first to get the equation in one variable.

Step 3:

• Solve this new equation to get the value of variable.

Step 4:

• Substitute value of this variable into either equation 1 or equation 2 to get the value of other variable.